The effects of spatial heterogeneity on the dynamics of reaction-diffusion models have been
studied extensively. In particular, global dynamics of general spatially heterogeneous (but
temporally static) Lotka–Volterra competition-diffusion systems were completely clarified by
He and Ni in 2016. However, the evolutionary impacts of temporal periodicity combined with
spatial heterogeneity in population ecology remain a challenging issue. In this work, we
consider a population model of two competing species in a both spatially varying and …